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Envelope solitons with fast oscillation in monatomic and diatomic chain
Nonlinear science abstracts
409
Other As a consequence, Eq. (2) will be recovered . is developed. hyperbolic equations and systems having a less simple form will also be considered and treated in an analogous fashion. method
INTEGRABILITY, Jarmo Hietarinta, Department of QUANTUM VS. CLASSICAL Physical Sciences, University of Turku, 20500 Turku 50, FINLAND. two degrees of freedom the integrability of We will discuss Using phase-space in classical and quantum mechanics. Hamiltonian systems representation and Moyal brackets the quantum problem can be written in terms of The differences between classical and quantum integrability c-number functions. is discussed with examples. ENVELOPE SOLITONS WITH FAST OSCILLATION IN MONATOMIC AND DIATOMIC CHAIN, N. Flytzanis, Physics Department, University of Crete, Iraklion, GREECE; Laboratoire d'optique du Reseau M. Remoissenet, and St. Pnematicos, Cristallin, Faculte des Sciences, Universite de Dijon, FRANCE. We study the propagation of fast oscillating envelope solitary waves chains with cubic or quartic nonlinear potential and diatomic in monatomic terms. In the long wavelength approximation of the envelope one obtains the equation for the first order amplitude after using the derivative N.L.S. The excitations are long lived and their collisions are expansion method. Their scattering from mass defects will be discussed. quasielastic. of Antoni SOLITON SURFACES AND THEIR APPLICATIONS, Sym, Institute Theoretical Physics of Warsaw University U-l, Hoza 69, 00-681 Warszawa, POLAND. The association of soliton surfaces with a given soliton system is a neralization of the well known connection between pseudo-spherical surfaces in gs and the sine-Gordon eq. This may be done for any soliton system with its E This Lie algebra serves as linear problem of the semi-simple Lie algebra type. In the case of su(2) soliton surfaces. the ambient space for embedded solito 4 space and most of the lecture will be surfaces are embedded into su(2) : E devoted to this case. The following applications of soliton surfaces will be discussed: soliton surfaces as a territory of unification of 4 types of solvable 1) non-linearities (solitons, strings, spins and chiral models) by construction soliton exact solutions to solvable non-linearities 2) surfaces with emphasis on the application in vortex physics Gauge + space-time transformation invariance of soliton surfaces 3) example of topological charge for non-topological solitons (Mod. KdV eq). 4) A GEOMETRIC NOTION OF COMPLETE INTEGRABILITY, Basilis C. Kanthopoulos, Department of Physics, University of Crete, Iraklion, Crete, GREECE. The mapping f:M + N, f={fA}, of two manifolds with metrics (M,g,) and (N,gAB) is called harmonic when it satisfies the equations gmnDmDnfA + $,(B
fB)(D; fC)gmn = 0,
where A=1,2,..., n=dimN, dm is the covariant derivative of (M,g,,) and I& are Harmonic mapping can be used to express the Christoffel symbols of (N,gAB). geometrically - i.e. in terms of the metrics gmn and gAB - certain classes of second order partial differential equations which arise in systems of The geodesics and the Killing fields of gAB provide, mathematical physics.
409
Other As a consequence, Eq. (2) will be recovered . is developed. hyperbolic equations and systems having a less simple form will also be considered and treated in an analogous fashion. method
INTEGRABILITY, Jarmo Hietarinta, Department of QUANTUM VS. CLASSICAL Physical Sciences, University of Turku, 20500 Turku 50, FINLAND. two degrees of freedom the integrability of We will discuss Using phase-space in classical and quantum mechanics. Hamiltonian systems representation and Moyal brackets the quantum problem can be written in terms of The differences between classical and quantum integrability c-number functions. is discussed with examples. ENVELOPE SOLITONS WITH FAST OSCILLATION IN MONATOMIC AND DIATOMIC CHAIN, N. Flytzanis, Physics Department, University of Crete, Iraklion, GREECE; Laboratoire d'optique du Reseau M. Remoissenet, and St. Pnematicos, Cristallin, Faculte des Sciences, Universite de Dijon, FRANCE. We study the propagation of fast oscillating envelope solitary waves chains with cubic or quartic nonlinear potential and diatomic in monatomic terms. In the long wavelength approximation of the envelope one obtains the equation for the first order amplitude after using the derivative N.L.S. The excitations are long lived and their collisions are expansion method. Their scattering from mass defects will be discussed. quasielastic. of Antoni SOLITON SURFACES AND THEIR APPLICATIONS, Sym, Institute Theoretical Physics of Warsaw University U-l, Hoza 69, 00-681 Warszawa, POLAND. The association of soliton surfaces with a given soliton system is a neralization of the well known connection between pseudo-spherical surfaces in gs and the sine-Gordon eq. This may be done for any soliton system with its E This Lie algebra serves as linear problem of the semi-simple Lie algebra type. In the case of su(2) soliton surfaces. the ambient space for embedded solito 4 space and most of the lecture will be surfaces are embedded into su(2) : E devoted to this case. The following applications of soliton surfaces will be discussed: soliton surfaces as a territory of unification of 4 types of solvable 1) non-linearities (solitons, strings, spins and chiral models) by construction soliton exact solutions to solvable non-linearities 2) surfaces with emphasis on the application in vortex physics Gauge + space-time transformation invariance of soliton surfaces 3) example of topological charge for non-topological solitons (Mod. KdV eq). 4) A GEOMETRIC NOTION OF COMPLETE INTEGRABILITY, Basilis C. Kanthopoulos, Department of Physics, University of Crete, Iraklion, Crete, GREECE. The mapping f:M + N, f={fA}, of two manifolds with metrics (M,g,) and (N,gAB) is called harmonic when it satisfies the equations gmnDmDnfA + $,(B
fB)(D; fC)gmn = 0,
where A=1,2,..., n=dimN, dm is the covariant derivative of (M,g,,) and I& are Harmonic mapping can be used to express the Christoffel symbols of (N,gAB). geometrically - i.e. in terms of the metrics gmn and gAB - certain classes of second order partial differential equations which arise in systems of The geodesics and the Killing fields of gAB provide, mathematical physics.